"Not in onomastics works, which are linguistic matter."
In that case, this conversation would not have started: Hindu is not a language, and neither is Indian. (Indian is as much a language as European is!)
"And Basque names are used not only by Basques (in North and in South) or Spanish, but in Idaho... are they Basque names or are they American names? A Basque name is a name in Basque, used in Bilbao, in Barcelona or in Bloise." and "the adjective refers to geographical origin and not to linguistic adscription"
There was nothing geographical in what I said: I said the adjective refers to the culture. A nation is not defined, at least since the rise of the modern era, politically, but by the identity of the people, both internally and externally. A Bengali moving to the US is still a Bengali till (s)he becomes American. I think it is a narrow view perhaps motivated by an European sensibility, where the prime attribute of culture relevant for onomastics is the language use, to consider only that aspect of culture.
You know much more of this subject than I do. I can only point out that if, indeed, onomastics is using a linguistic adjective where it should be using a cultural one, it is making a mistake. An Southwest American usage in name can be different from a Northeastern one not because they speak different languages, though they might, but *because* they are somewhat separate cultures. Similarly, a Judeo-christian tradition binding most of the western world reflects itself in naming patterns. A study of names which ignores this in its standard vocabulary, is making it harder than it should for people to express facts about names clearly.
I had always thought an Irish name was a name traditionally used by the Irish, whether or not it can be traced to any Gaelic feature, Irish or otherwise. It just happened that this coincided with names that are either Irish in the linguistic sense, or whose phonological pattern has been made Irish.